The optimal hedge ratio (OHR) is an important tool for hedging against the price risk. A number of different approaches have been utilized in the literature in order to estimate the OHR, among others, constant parameter and time-varying approaches. One relevant question in this regard that has not been examined, to the best knowledge, is whether the OHR has an asymmetric structure or not. This issue is addressed in the current paper by mathematically proving that the OHR is asymmetric. Furthermore, we offer a method to deal with this asymmetry in the estimation of the underlying OHR. This method is applied to the US equity market using weekly spot and future share prices during the period January 5, 2006 to September 29, 2009. We find empirical evidence that supports the existence of an asymmetric OHR.